Monday, March 20, 2017

In randomized
controlled clinical trials, we usually need to consider if there are any prognostic
factors that may have influence on the primary outcome measure. The prognostic
factors usually include demographic information (gender, age), severity of the
disease (mild, moderate, and severe), use of concomitant medication (patients
on background therapy versus patients not on background therapy), genetic
sub-type of the disease, biomarker measures at baseline…

Dealing
with the prognostic factors can be at the statistical analysis stage through
the sub-group analyses to investigate the impact of the prognostic factors on
the treatment outcome.

However,
if there are factors known to have impact on the treatment outcome, it is better
to consider them in the planning stage through the stratified randomization.
The prognostic factors are considered as stratified factors. In stratified
randomization, the random treatment assignment is actually performed within
each strata. I had an old blog article to explain the stratified randomization “Stratified randomization to achieve
the balance of treatment assignment within each strata”

When
we plan for the stratified randomization, the number of stratification factors
and number of levels or categories for each stratification factor need to be
considered. The total number of strata is the multiplication of the number of
levels of stratification factors.

Suppose
we just have one stratification factor with two levels (age group: 'less than 65 years
old' versus 'greater than and equal to 65 years old'), the total number of strata = 1 x 2 = 2. The
randomization (specifically the block randomization) will be implemented within
each stratum of 'less than 65 years old' or 'greater than and equal to 65 years old'.

Suppose
we have two stratification factors: age group with two levels ('less than 65 years old' versus 'greater than and equal to 65 years old') and disease severity with three levels (mild,
moderate, and severe), the total number of strata = 2 x 3 =6. The randomization
(specifically the block randomization) will be implemented within each of the
following 6 strata (combinations):

less than 65
years old and mild severity

less than 65
years old and moderate severity

less than 65
years old and severe severity

greater than and equal to 65
years old and mild severity

greater than and equal to 65
years old and moderate severity

greater than and equal to 65
years old and severe severity

The
question arises when more and more stratification factors are added to the
list. How many stratification factors can we have in a study while still
maintaining the overall balance in treatment assignment across all of these
strata?

The
number of strata can increase rapidly. Suppose we have three stratification
factors:

Age
group with two levels ('less than 65 years old' versus 'greater and equal to 65 years old')

Disease
severity with three levels (mild, moderate, and severe)

Geographic
region with four categories (Asia, Europe, North America, and South America)

The
total number of strata = 2 x 3 x 4=24. The randomization (specifically the
block randomization) will be implemented within each of the 24 strata
(combinations):

less than 65
years old, mild severity, Asia

less than 65
years old, moderate severity, Asia

less than 65
years old, severe severity, Asia

……

While
there is not rule how many stratification factors or strata can be used in a
clinical trial, I usually stick with a number to keep the number of
stratification factors no more than two or total number of strata no more than
6.

With
the limited total sample size, if there are too many stratification factors or
too many strata, it can actually cause the imbalance in treatment assignment on
the study level. Even though the treatment assignment is intended to be
balanced within each stratum by implementing the block randomization, there
will be always incomplete blocks across all strata, which causes the imbalance
in treatment assignment on the study level.

One
approach to address this issue is an approach called ‘minimization’ algorithm.
Minimization algorithm is one of the adaptive randomization approaches. It is
used in the situation where there is a limited or small overall sample size,
but many critical stratification factors.

Here are a couple of screen shots for illustrating how the minimization works.

The
minimization requires the calculation after each subject is randomized. It is
almost not possible to implement the minimization with the manual process. Luckily,
with IRT (Interactive Response Technology) including IVRS (interactive voice
response system) and IWRS (interactive web response system), the minimization
can be implemented through programming. The algorithm for minimization is built
into the IRT system and the calculation after each subject randomization is
automatically calculated by the system. The IRT vendors such as conduit, sovuda, Datatrak et al can all do
the implementation of the minimization algorithm.